Mapping the response of volumetric soil water content to an intense rainfall event at the field scale using GPR

Journal of Hydrology 583 (2020) 124605

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Research papers

Mapping the response of volumetric soil water content to an intense rainfall event at the field scale using GPR

T

Qi Caoa,b,1, Xiaodong Songa,1, Huayong Wua, Lei Gaoa, Feng Liua, Shunhua Yanga,b, ⁎ Ganlin Zhanga,b, a b

State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences, Nanjing 210008, China University of Chinese Academy of Sciences, Beijing 100049, China

A R T I C LE I N FO

A B S T R A C T

This manuscript was handled by Emmanouil Anagnostou, Editor-in-Chief, with the assistance of Georgia Destouni, Associate Editor

Ground-penetrating radar (GPR) is a convenient tool for volumetric soil water content (VSWC) estimation in hydrological and agricultural studies. Although case studies have been widely carried out, little attention has been paid to subsoil moisture estimates. In this research, we investigated three-dimensional soil moisture variation down to a depth of 1 m and the effect of rainfall events on spatial soil moisture dynamics. GPR surveying lines were conducted both before and after a heavy rainfall event to map the VSWC. Soil sampling and time domain reflectometry (TDR) probe data at different depths (20, 40, 60, 80, and 100 cm) were acquired. Our results demonstrated that there was a significant correlation between the dielectric constants and VSWCs at all depths. The established relationships for the different depth ranges had a low VSWC discrepancy when the dielectric constants ranged from 10 to 15. The effective range of each variogram was larger than 20 m, except for that of the 0–100 cm VSWC map after rainfall. In addition, the validation diagrams using corrected TDR values demonstrated relatively reliable VSWC maps. Approximately 89% of the variation in VSWC could be explained by the dielectric constants in the depth range of 0–40 cm, and VSWC predictions at this soil depth outperformed those at other depth ranges, with an overall RMSE of 0.027 m3 m−3 and R2 of 0.725. Furthermore, we also monitored the effect of precipitation on the accuracy of the VSWC prediction on shallow surfaces. Our study shows that three-dimensional soil moisture dynamics can be accurately estimated at the field scale by integrating GPR interpretation and spatial extrapolation methods.

Keywords: Ground wave method Soil water content Subsoil Geostatistics Red soil

1. Introduction Soil water content is a vital indicator to characterize Earth’s critical zone and is an essential parameter in climatology, hydrology, agriculture, and meteorology studies (Lin, 2010; Kirkby, 2016; Vereecken et al., 2016). However, characterizing midscale soil water dynamics has remained a challenge because of the considerable spatial heterogeneity of soil horizons, soil texture and agricultural management practices (Klenk et al., 2015). There are many methods for measuring soil moisture at the point scale, including the gravimetric method, the neutron method, the γ-ray method, and time domain reflectometry (TDR) (Robinson et al., 2008). These methods are relatively time consuming, laborious and destructive to the soil. The satellite remote sensing method, which is easily affected by vegetation cover, can obtain the topsoil water content distribution at the regional scale (Starks et al., 2006; Wang and Qu, 2009). Because of their inappropriate

investigation scopes, depth and resolution, these two types of methods cannot adequately capture detailed soil hydrodynamic behavior at the midscale (i.e., field or catchment). Over the last twenty years, electromagnetic geophysical methods, including electric resistivity tomography and ground-penetrating radar (GPR), have been used to bridge that gap (Binley et al., 2002; Deiana et al., 2008; Brunet et al., 2010; Wijewardana and Galagedara, 2010; Garré et al., 2012; Shamir et al., 2016). In particular, GPR offers the advantages of nondestructive, high-precision measurements and a large depth of detection, and it is suitable for a variety of geological conditions. The application of different GPR techniques is increasing (Weihermüller et al., 2007). Cross-borehole GPR has been successfully employed for finding preferential flow paths (Klotzsche et al., 2012; Zhang et al., 2014) and estimating soil moisture content and hydraulic properties based on coupled inversion models (Kowalsky et al., 2004; Haarder et al., 2012; Gueting et al., 2017). In recent years, the vertical

⁎

Corresponding author at: State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences, Nanjing 210008, China. E-mail address: [email protected] (G. Zhang). 1 These authors contributed equally to this work and are co-first authors. https://doi.org/10.1016/j.jhydrol.2020.124605 Received 30 March 2019; Received in revised form 30 September 2019; Accepted 19 January 2020 Available online 23 January 2020 0022-1694/ © 2020 Elsevier B.V. All rights reserved.

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2.2. Soil analysis

radar profile technique has been shown to be more convenient than cross-borehole radar due to the presence of a single borehole, but this method must avoid emerging direct waves that interfere critically with refracted waves (Strobach et al., 2014; Tronicke and Hamann, 2014). Lambot and Andre (2014) developed an off-ground (i.e., air-launched) GPR technique to calculate the shallow subsurface soil hydraulic properties in near-field conditions, but off-ground radar is restricted to surface roughness. In addition, traditional on-ground GPR has been widely used to measure the volumetric soil water content (VSWC). Pan et al. (2012) found that the spatiotemporal variations in soil moisture in typical farmland were related to vegetation growth. Steelman and Endres (2011) conducted complete field research on three soil textures using the high-frequency direct ground wave method. A number of studies have reported that the GPR ground wave technique is a common way to monitor shallow VSWC compared to the results of the TDR and gravimetric methods (Galagedara et al., 2005; Klenk et al., 2011; Steelman et al., 2012). The more suitable the empirical formula between the dielectric constant and the VSWC is, the higher the detection accuracy of GPR. Empirical equations based on indoor simulated tests (Topp et al., 1980; Roth et al., 1992), volumetric mixing formulas (Dobson et al., 1985; Herkelrath et al., 1991) and effective medium-rough evaluations in view of soil models (Sen, 1984; Endres and Bertrand, 2006) have been attempted to convert the dielectric constant into VSWC. However, many of these relationships have not yet been calibrated in the field using GPR technology. Therefore, it is necessary to collect GPR measurements in situ and obtain actual calibrated petrophysical relationships for the estimation of VSWC. The sampling depths and time-zero calibration in complicated soil types are also a concern for the GPR ground wave method. Steelman and Endres (2011) demonstrated that the GPR sampling depth was affected by the antenna frequency and soil texture. Meanwhile, surface roughness, tillage management and bedrock distribution may be potential factors affecting GPR measurements (Jonard et al., 2012; Ardekani, 2013; Jonard et al., 2013). Many studies could retrieve VSWC at only a single depth due to the limited experimental time and verification techniques (Grote et al., 2003; Steelman and Endres, 2010). Consequently, it is necessary to develop proper empirical models for ground wave methods for various soil depth ranges. In this study, the application of the GPR ground wave technique was investigated to quantify field-scale VSWC dynamics. The petrophysical empirical relationships of different depth ranges were quantified to enhance the measurement accuracy, in which the GPR sampling depth and time-zero calibration were achieved under the common midpoint (CMP) survey mode. The effects of land use and precipitation on the spatial pattern of VSWC were determined.

The soils in the Sunjia watershed were dominated by Ultisol based on USDA Soil Taxonomy (Soil Survey Staff, 2010). Six soil profiles were excavated to help determine the soil properties (Fig. 1). Mixed and undisturbed soil samples were collected from the uplands and orchards with a 100 cm3 cutting ring with three replicates each at 0–20, 20–40, 40–60, 60–80 and 80–100 cm depths in January 2018. The mixed soil was used to determine the particle size distribution (clay, < 2 μm; silt, 2–50 μm; and sand, 50–2000 μm) using a laser grain-size analyzer (Beckman Coulter LS230, USA) after pretreatment, including air drying, grinding and passing through a 2 mm sieve. The cutting ring soil samples were used to obtain the soil bulk density. Detailed information regarding the soil properties is presented in Table 1. 2.3. VSWC data collection In the sampling area, custom-built polyvinyl chloride pipes (diameter: 0.05 m; length: 2 m) were installed at 32 sites (Fig. 1). We measured the VSWC at depths of 0–20, 20–40, 40–60, 60–80 and 80–100 cm using a matched portable Bluetooth probe (IMKO TDR, Ettlingen, Germany). The success or failure of the representation of the VSWC by TDR depends on the accuracy of the invoked calibration. Because our TDR accuracy was 2%, the mass soil water contents of the soil samples at the same depth were calculated by weight loss at 105 ± 3 °C after oven-drying for at least 24 h. The TDR calibration, y = 0.94x + 0.0176, was obtained from the gravimetric method data, and the coefficient of determination (R2) value was 0.88. The average VSWCs of the 0–20, 0–40, 0–60, 0–80 and 0–100 cm depths were used for the GPR sampling depth analysis. The TDR and GPR measurements were carried out simultaneously. Due to the limited soil profiles, we analyzed the correlations between VSWCs and soil properties at different depths together (Fig. 2). A significant negative correlation was found between VSWC and sand content (p < 0.05) (Fig. 2a), whereas VSWC was positively correlated with silt content (p < 0.05) (Fig. 2b), which was consistent with recent studies (Fang et al., 2016; Lai et al., 2018; Wang et al., 2019). In theory, when the soil water contents of the 0–20 and 20–40 cm depths are known, the soil water content of the 0–40 cm depth can be calculated using an average function. The VSWC from the surface soil to a depth could be computed by weighing the VSWC at fixed depth increments (e.g., 20 cm), as specified in Eq. (1).

θ0_d

20 = × d

d 20

∑ θ20(i −1)_20i

(d = 40, 60, 80, 100)

i=1

(1)

where d is the soil depth (cm) and θ0_d is the VSWC at a depth of 0–d cm. Furthermore, the VSWCs at soil depth ranges of 20–40, 40–60, 60–80 and 80–100 cm could be iteratively derived by Eq. (2).

2. Materials and methods

d d θd _(d + 20) = θ0_(d + 20) × ⎛ + 1⎞ − θ0_d × (d = 20, 40, 60, 80) 20 ⎝ 20 ⎠

2.1. Study area

(2)

where θd_(d+20) is the VSWC at a depth of d ~ (d + 20) cm. The study area (~3.2 ha) is an agricultural field located in the Sunjia watershed in the southern part of Yingtan City, Jiangxi Province, China (Fig. 1), which has been established as the Red Soil Critical Zone Observatory (Tahir et al., 2016; Wu et al., 2019). This area is characterized by a subtropical monsoon climate, with a mean annual precipitation of 1795 mm, a mean annual temperature of 17.8 °C and a frost-free period of 258 days (Gao et al., 2016). The slope of the watershed is approximately 6°, and the altitude is between 53.4 and 61.1 m. Quaternary red clay and red sandstone are the parent materials. Upland and citrus orchards are common land use types in the study area, accounting for 79% and 19%, respectively (Gao et al., 2016; Tahir et al., 2016).

2.4. GPR system and ground wave method 2.4.1. Ground wave method In this study, a geological radar (AKULA-9000C, Sweden) was used that had two 60 MHz bowtie transmitting (T) and receiving (R) antennas. The ground wave method includes two measuring modes: CMP and fixed offset (FO). The effective detection depth is inversely proportional to the antenna frequency of the radar. The lower the antenna frequency is, the deeper the detection depth. In general, the effective detection depth of the 60 MHz antenna is greater than 8 m, which fully meets the depth requirements of this study. Correlation analysis between dielectric constants and observed VSWCs at different soil depths 2

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Precipitation [mm/d]

60

50

50

40

40 30 30 20

20

Before rainfall

After rainfall

10

10

0 0 18 19 20 21 22 23 24 25 26 27 28

Days in July 2018

Fig. 1. (a) Study site (red triangle) in Yujiang County, Yingtan City, (b) daily precipitation and daily average temperature in the Sunjia watershed in July 2018, and (c) the TDR point locations (n = 32) and radar lines in our study area. Note that black arrows in (b) represent the first (before rainfall) and second (after rainfall) measurement times. The red dots in (c) indicate the TDR locations. The midpoints of the CMP lines (5 m) are very close to the TDR locations and are not shown. The blue lines indicate the FO measurements, over which the distance interval between sampling points is 3 m and these points are not displayed due to their high density. The black numbers around the contour lines indicate the elevation (m). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 1 Statistics of soil physical properties (mean ± standard deviation) from six soil profiles. Depth (cm)

Clay (%)

0–20 20–40 40–60 60–80 80–100

20.30 20.80 21.80 22.90 23.25

± ± ± ± ±

Silt (%) 3.19 2.77 2.57 2.35 1.49

48.65 50.70 50.45 54.25 49.25

± ± ± ± ±

Sand (%) 3.98 3.78 1.60 1.63 1.16

31.05 28.50 27.75 22.85 27.50

± ± ± ± ±

Bulk density (g cm−3)

Silt/clay 6.42 1.78 2.82 2.89 1.34

2.43 2.50 2.35 2.39 2.13

± ± ± ± ±

0.30 0.55 0.35 0.26 0.16

1.36 1.41 1.43 1.45 1.46

± ± ± ± ±

0.02 0.04 0.06 0.01 0.04

inferred by the slope of the ground wave from the radargram (Fig. 4a). The dielectric constant, ε, is calculated using the following equation:

was performed to verify whether the VSWC could be significantly detected and which depth range was the most accurate. When passing through a complicated soil medium, electromagnetic waves are emitted by the transmitting antenna; then, the air, ground, reflected, and refracted waves are distinguished by the receiving antennas (Fig. 3). The radar signal at each measurement point was recorded with a time window of 400 ns by stacking 24 scans and discretizing 600 samples. A dewow 1D filter and static correction were used to obtain the critical information. The automatic gain control (AGC) gain was applied to each radar trace to strengthen the signals in deep soil. Then, we used the finite impulse response method to retain the Ricker-type electromagnetic pulse with a 25–130 MHz frequency bandwidth. The CMP measurements were carried out to estimate the GPR sampling depth of the VSWC, calibrate the time-zero (t0) of the ground wave and fit a suitable petrophysical relationship. The transmitting and receiving antennas shifted in opposite directions (Fig. 3c), in which the total length of one surveyed line was 5 m and the moving step length of each antenna was 0.05 m. When zero antenna offset occurs, the air wave and ground wave will not be received simultaneously due to the radar configuration (Huisman et al., 2001; Steelman and Endres, 2010). The propagation velocity of the electromagnetic wave (v) could be

c 2 ε≈⎛ ⎞ ⎝v⎠

(3)

where v is the speed of the ground wave and c is the propagation velocity of the electromagnetic wave in a vacuum (0.3 m ns−1). Since the ground wave is transmitted from the transmitting antenna to the receiving antenna through the surface soil, the effective inversion depth of the ground wave method starts at 0 cm. Single trace analysis was commonly used to obtain the electromagnetic wave velocity from on-ground radar signals in FO mode (Huisman et al., 2001; Galagedara et al., 2003) (Fig. 3d), in which the transmitting and receiving antennas moved in the same directions (Fig. 3d). The arrival time of the air wave (tAW) and ground wave (tGW) at 1.0 m antenna separation can be captured to calculate the velocity of electromagnetic waves (v) through the surface soil (Fig. 4b):

x ⎞ ⎛ v =⎜x ⎟ + ( t − t − t ) GW 0 AW ⎠ ⎝c where x is the antenna spacing (1.0 m) and t0 is time-zero. 3

(4)

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Fig. 2. Scatter plots of the VSWC and sand content (a) and VSWC and silt content (b). Note that soil data at different depths were analyzed together due to limited soil profiles.

while the FO method was convenient, fast and suitable for large-scale measurement. Notably, there was little difference between the dielectric constants obtained by the CMP method and those obtained by the FO method (Huisman et al., 2003). Thus, GPR data from the CMP method were adopted as the baseline for calibrating the time-zero and the fit of the empirical function between VSWCs and dielectric constants. These empirical functions were utilized to calculate VSWC data based on the dielectric constants derived from the FO method, and the new VSWC data were then used to predict the spatiotemporal variations in VSWC. For both experiments, we considered different land use types and spatiotemporal variability. The CMP experiment was conducted during three time periods: 14–16 January, 15–17 March and 17–18 July 2018, and VSWC data were recorded simultaneously. The midpoint of the

2.4.2. GPR data collection In the current study area, the top 1 m of soil (uniform red clay) was characterized by homogeneous granular aggregates that could be considered to be clay loam (Wu et al., 2019), and the soil texture was generally invariable along the soil profiles (Table 1) (Gao et al., 2016). It could be inferred that the magnetic properties of the top 1 m of soil were similar or even the same, as they had very similar color (Hu et al., 2014), subsurface structure (Wu et al., 2019) and clay minerals (Tang et al., 2008). Thus, it was assumed that the dielectric constants were the same in the top 1 m of soil. Data collection was divided into two experiments: CMP measurement and FO measurement. One CMP surveying line could derive only one dielectric constant, while one FO line could derive many dielectric constant values. The CMP method was accurate but time consuming,

(a)

(b)

T

R

Air Wave

Ground Ground Wave

Refracted Wave /Lateral Wave

Reflected Wave

Reflector

(c)

T2

T1

R1

R2

(d)

x1 x2 t2

T1

R1

T2

x

R2

x

t1 Direction

Direction

T R

T R FO Measurement

CMP Measurement

Fig. 3. An illustration of the GPR survey mode in this study: (a) equipment for the GPR field surveys, (b) schematic map of electromagnetic wave propagation in ideal soil, and a schematic diagram of the CMP measurement (c) and FO measurement (d). T and R indicate the transmitting antenna and receiving antenna, respectively. 4

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b)

AW

25 50

t0

GW 75 100

Travel time (ns)

Travel time (ns)

a) 0

0

tAW

30

tGW

60 90 120

0

1

2

3

4

5

0

20

40 Distance (m)

Distance (m)

60

80

Fig. 4. GPR CMP (a) and FO (b) radar profiles. AW and GW indicate the air wave and ground wave, respectively.

analysis, mapping and map visualization were performed using SAS 9.2 software, R 3.3.1 with packages “gstat” and “raster”, and ArcGIS 10.3 software, respectively. The formula between the dielectric constants and VSWCs was fitted with Origin 8.6 software.

CMP line was very near one TDR site (approximately 10–20 cm) rather than directly passing through the TDR site (Fig. 1), as buried pipes will affect the propagation of electromagnetic waves. A total of 32 CMP soundings were conducted and thus 32 dielectric constant values were obtained, which can correspond to each TDR value. The mean timezero, t0, was calculated from the wavelet (Fig. 4a). The propagation velocity of radar waves was estimated by the velocity stack in a constant velocity earth (Travassos and Menezes, 2004; Forte and Pipan, 2017), and the dielectric constant was further derived by Eq. (3). FO measurements are the key to achieving regional soil water content observations. All two-dimensional GPR FO surveying lines were conducted with 1.0 m antenna separation on 21 and 25 July 2018 (Fig. 1c). We adopted duplicated measurements to control the survey quality. The electromagnetic wave information was recorded per 1 m in the field. The dielectric constant was calculated from these electromagnetic waves every 3 m, in which adjacent waves were not used for the calculation but for data quality control. For example, 10 dielectric constants can be generated from a 30-m FO line. In addition, if one measurement point was very near the TDR location, electromagnetic waves at this point were recorded three times, and the average value was taken as the final result. Finally, a total of 324 paired sample points were obtained from 12 radar lines (Fig. 1c) before and after rainfall events. We did not show the spatial distribution of these points, as the interval of adjacent points was 3 m and the high sampling density would crowd Fig. 1. The propagation velocity of the ground wave can be calculated by incorporating the parameters of arrival time (i.e., tAW and tGW) (Fig. 4b) into Eq. (4).

3. Results 3.1. Effective sampling depth of the GPR ground wave method As described in Section 2.4.1, the effective sampling depth was verified in accordance with the correlation coefficient (r) (Table 2), which was obtained from linear regression analysis of the in-situ-calibrated VSWCs of TDR and the soil dielectric constants (ε) obtained from 32 CMP soundings. The r values were greater than 0.53 in all depth ranges and were greater than 0.74 when the depth of the bottom layer was < 60 cm. It was suggested that there was a strong correlation between the dielectric constant of the ground wave and the VSWC in different layers. This result was different from that of Steelman and Endres (2011), which might be ascribed to the low frequency of radar antennas and the small difference in the soil water content in the homogeneous laterite layer. 3.2. The suitable petrophysical relationship The VSWCs in the depth ranges of 0–20, 0–40, 0–60, 0–80 and 0–100 cm were computed according to Eq. (1). Five empirical nonlinear formulas between the dielectric constants and VSWCs at these five depths were established, which were referred to as F0_20, F0_40, F0_60, F0_80 and F0_100:

2.5. Statistical and geostatistical analyses

F0_20:

One-way analysis of variance (ANOVA) was adopted to test if the VSWC was significantly different at five soil depths (p < 0.05). The normality of the dependent variable should be evaluated before spatial prediction. In this study, the derived VSWC values were normally distributed through the analysis of quantile–quantile (QQ) plots and histograms. All VSWC data at different soil depths exhibited a square trend when performing the trend analysis. The VSWC values derived by the FO method were interpolated by ordinary kriging (OK). OK is a widely used geostatistical model that uses a series of statistical tools to predict the soil properties (VSWC in this study) at unsampled locations. A semivariogram is a continuous function for describing the spatial variability of soil properties. Positive definite models, exponential functions and automated fitting procedures were used to approximate the variograms. Spatial interpolations were evaluated by TDR values in terms of the correlation coefficient (r), R2 and root mean square error (RMSE). The spatial heterogeneity of VSWCs was quantified by statistical indices, such as the maximum, minimum, average values, standard deviation (STD) and coefficient of variation (CV). GPR data were processed in Reflexw 8.5 software. The statistical

θ0_20

= −2.68 × 10−1 + 8.67 × 10−2ε − 4.8 × 10−3ε 2 + 9.1 × 10−5ε 3 R2 = 0.66 (5)

F0_40:

θ0_40

= −2.23 × 10−1 + 7.67 × 10−2ε − 4.17 × 10−3ε 2 + 8.31 × 10−5ε 3 = 0.89

F0_60:

R2 (6)

θ0 − 60

= 1.48 × 10−1 + 1.26 × 10−4ε + 8.8 × 10−4ε 2 − 2.29 × 10−5ε 3

R2 (7)

= 0.67

Table 2 Correlation coefficients (r) between the calibrated VSWC of TDR and the dielectric constant (ε) from the ground wave velocity measurements. Depth (cm)

0–20

0–40

0–60

0–80

0–100

r

0.742***

0.916***

0.820***

0.567***

0.538***

*** Extremely significant correlation at the 0.001 level. 5

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F0_80:

Regarding the F0_20 model, the after-rainfall variogram was characterized by a higher nugget/sill ratio (54.3%) and a larger range (27.4 m), which suggested that the spatial variability among the samples was due to random factors. Conversely, the nugget/sill ratio and range were smaller before rainfall (36.0% and 21.8 m, respectively), indicating strong spatial dependence. In addition, the F0_40, F0_60 and F0_80 models showed results similar to the F0_20 model. The kriging results for these models after rainfall had a long range (26.6, 26.6 and 35.8 m, respectively) and a high nugget/sill ratio (48.2%, 49.1% and 57.8%, respectively). However, a smaller nugget/sill ratio (1.5%) was found in the after-rainfall F0_100 model. The lower the nugget/sill ratio is, the stronger the spatial dependence structure (Lado et al., 2008). Fig. 8 shows the OK mapping results for the VSWC on 21 and 25 July, in which the same color scale is used. The nine VSWC maps on 21 July showed a similar spatial pattern, in which high VSWC values were found at the highest and lowest elevations. The upland in the middle of a slope appeared drier than its upper and lower portions. The fieldaverage VSWC was equivalent to 0.255 m3 m−3 for the 0–20 cm soil layer, with a CV of 4.7% (Table 3). When the depth ranged from 0–20 to 0–100 cm, the average VSWC increased from 0.255 to 0.276 m3 m−3, and the CV increased from 4.7% to 9.2%. Regarding the 20–40, 40–60, 60–80 and 80–100 cm depths, the mean VSWC was approximately equal to 0.28 m3 m−3, and the CVs were 10.1%, 9.6%, 11.8% and 11.2%, respectively. The VSWC maps derived from the 0–40, 0–60, 0–80 and 0–100 cm relationships on 25 July showed high VSWC values in almost all of the field areas. The average VSWC was 0.272 m3 m−3 in the 0–20 cm layer after rainfall. Low soil moisture levels were found on both sides of the road and near drainage ditches. The VSWC distribution pattern of the 20–40 cm layer was different from those of the 40–60, 60–80 and 80–100 cm layers and had a high soil water content near the zone boundary (Fig. 8). Meanwhile, the VSWC differences before and after rainfall were further compared in space (Fig. 9). After rainfall, the water content of all the soil layers increased over a large area, mainly in the depth range of 20–40 cm. The proportions of VSWCs that decreased, that is, the VSWCs with differences < 0 as computed by ArcGIS 10.3 software, were found to be 12.4%, 8.7%, 33.6%, 43.1% and 50.2%, respectively, for the 0–20, 20–40, 40–60, 60–80 and 80–100 cm soil masses. The soil water content decreased in some places, such as ridges and field paths. Land use type had a noticeable influence on the soil water content changes. The upland area had a greater water content increase than the orchard in the 0–20, 20–40, 40–60 and 80–100 cm depths, with mean VSWC differences of 0.019, 0.048, 0.034 and 0.023 m3 m−3, respectively.

θ0_80

= 3.81 ×

10−1

− 5.12 ×

10−2ε

+ 4.45 ×

10−3ε 2

− 1.01 ×

10−4ε 3

R2 (8)

= 0.47

F0_100:

θ0_100

= 2.74 × 10−1 − 3.61 × 10−2ε + 3.86 × 10−3ε 2 − 9.58 × 10−5ε 3

R2 (9)

= 0.58

where ε denotes the dielectric constant of the top 1 m of soil, and θ0_20, θ0_40, θ0_60, θ0_80 and θ0_100 denote the VSWCs at soil depths of 0–20, 0–40, 0–60, 0–80 and 0–100 cm, respectively. The fitting results of these five models showed that at least 47% of the VSWC could be accounted for. Interestingly, the R2 was 0.89 for the F0_40 model and declined to 0.66 for the F0_20 model. The surface roughness of the 0–20 cm soil was frequently affected by agricultural tillage, which may change the propagation path of the electromagnetic wave and thus lead to poor fitting. The R2 of the F0_60 model was 0.67, but the R2 of the F0_80 model was only 0.47. This difference may be due to the existence of a compacted layer with more soil moisture between 60 and 80 cm, which makes electromagnetic waves more easily attenuated. When the electromagnetic waves passed through the compacted layer, the R2 of the F0_100 model moderately increased to 0.58. These models are presented in Fig. 5 for visual comparison, in which the soil dielectric constant ranges from 5 to 25. The petrophysical relationships optimized by data from the five depths (Eqs. (5)–(9)) had small differences when the dielectric constant was between 10 and 15. In other ranges, the difference was large. 3.3. In situ VSWC before and after rainfall The impact of rainfall events on the VSWC was investigated based on the VSWC of TDR (n = 32) on 21 and 25 July 2018 (Fig. 6). Fig. 6a. shows the calibrated average VSWCs and the standard errors for five layers with the same depth increments. The average VSWC for the 0–20, 20–40 and 60–80 cm depths increased to a certain extent (Fig. 6a). The VSWC for the 20–40 cm depth showed an approximately 21% increase due to this rainfall event. However, the soil water content in the 40–60 and 80–100 cm depth ranges decreased slightly. There were no significant differences between most treatments before and after rainfall. 3.4. Spatiotemporal variations in the VSWC derived from the ground wave FO method An exponential model and a 3 m lag distance were used to compute the variograms (Fig. 7). The effective range of the variograms was larger than 20 m except for the variogram of 0–100 cm after rainfall.

3.5. Accuracy evaluation

0.5 F0_20

To objectively assess the estimation accuracy, the VSWC values of the 0–20, 0–40, 0–60, 0–80 and 0–100 cm depths in Fig. 8 were compared with the calibrated TDR values (Fig. 10 and Table 4), and the subsoil VSWC maps at 20-cm intervals (e.g., 20–40 and 80–100 cm) were not validated. The overall validation in terms of R2 suggested an acceptable estimation (Table 4). Fig. 10a shows the validation diagram of the F0_20 model for both datasets together, with an overall RMSE of 0.046 m3 m−3 and R2 of 0.501. The F0_40 model yielded the best result, with an overall RMSE of 0.027 m3 m−3 and R2 of 0.725. The F0_60 model was in good agreement with the F0_40 model, except for having a smaller fitting curve slope, for which the overall RMSE and R2 were 0.028 m3 m−3 and 0.578, respectively. In contrast, the F0_80 and F0_100 model validation graphs had greater RMSE values of 0.032 m3 m−3 and 0.031 m3 m−3 and smaller R2 values of 0.395 and 0.335, respectively.

F0_40

VSWC (m3 m-3)

0.4

F0_60 F0_80 F0_100

0.3

0.2

0.1

0.0

5

10

15

20

25

Dielectric constant Fig. 5. Mathematical relationships between dielectric constants and VSWCs. 6

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(a)

(b) 0.5

0.6

Before rainfall After rainfall

0.5

0.4

ab abc

0.3

bc

ab ab

a

cd VSWC (m3 m-3)

VSWC (m3 m-3)

abc 0.4

Before rainfall After rainfall

abc a abc

c

0.2

0.3

d

d

c

ab

bc c

bc

ab

0.2

0.1

0.1

0.0

0-20

20-40

40-60

60-80

0.0

80-100

0-20

0-40

Depth (cm)

0-60

0-80

0-100

Depth (cm)

Fig. 6. VSWC ground truth (a) and VSWC after average conversion (b) before and after rainfall. Lower case letters above the bars represent significant differences (p < 0.05).

4. Discussion

In this study, all CMP lines were conducted near TDR locations. Therefore, a correlation analysis between dielectric constants derived from CMP lines and the VSWCs observed at different soil depths was performed. It was difficult to verify the effective depth of each CMP sounding. However, notably, this area was characterized by a similar soil texture in the horizon (Tang et al., 2008; Gao et al., 2015; Gao et al., 2016) (Table 1). We believed that the correlation analysis based on all CMP lines (Table 2) was credible enough for this study. To acquire the empirical model between the VSWC and the dielectric constant in a special study site, both GPR measurements were collected on undisturbed farmlands and validated with the corrected TDR method. Nevertheless, seasonal soil conditions and soil properties were also related to the GPR measurement (Steelman and Endres, 2011). The fitted petrophysical relationships may be limited to our study area or other similar areas, and thus, further study is needed to obtain a more appropriate empirical formula.

4.1. GPR sampling depth and petrophysical relationship Due to the different measurement locations, the ground-truth values of VSWC measured by the TDR and GPR ground wave methods were not always parallel before and after rainfall. GPR could represent the average VSWC between two antennas, whereas the TDR measurement was restricted to a small area near the probe (Whalley, 2010). A number of studies have shown that the field GPR antenna configuration and signal wavelength have an effect on the sampling depth of the ground wave method (Vanovermeeren et al., 1997; Huisman et al., 2003). For example, the sampling depth of the 450 MHz surface GPR can be within the 0–20 cm depth range (Grote et al., 2003). Furthermore, under different antenna frequencies and soil texture conditions, the GPR sampling depth analysis can be based on the highest R2 value (Steelman and Endres, 2011), which was equivalent to r in our study (Table 2). Our results showed that the VSWC value-derived ground wave method had a very good correlation with the TDR results of different depth ranges (Table 2), and five depth models had good prediction accuracy (Table 4). This result may be because the 0–1 m soil mass in the red soil area was a homogeneous laterite layer with the same soil properties and less change in the soil water content. This depth range could be regarded as the root zone of plants and crops, which is conducive to the growth and production of crops (Gao et al., 2013; Tahir et al., 2016).

(a)

To map and evaluate the impact of land use type on soil water content change, one traditional direct method was collecting soil drilling samples and conducting water content analysis at multiple locations. Nevertheless, the collection of high-resolution VSWC data using drilling was expensive and time consuming. Our study presented a convenient approach through monitoring the location at FO survey

0.0020

(b)

F0_20 F0_40

F0_20

After rainfall

F0_40 F0_60

0.0015

Semivariance

F0_80 F0_100

0.0010

0.0005

0.0000

0.0020

Before rainfall

F0_60

0.0015

Semivariance

4.2. Land use type and rainfall effect on the surface VSWC

F0_80 F0_100

0.0010

0.0005

0

25

50

75

0.0000

100

0

25

Distance (m)

50

Distance (m)

Fig. 7. Variograms for GPR-derived VSWC before and after rainfall. 7

75

100

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0~20 cm

Before rainfall

0~20 cm

0~40 cm

0~60 cm

0~80 cm

20~40 cm

40~60 cm

60~80 cm

0~40 cm

0~60 cm

0~80 cm

20~40 cm

40~60 cm

60~80 cm

0~100 cm

80~100 cm

0~100 cm

80~100 cm

After rainfall

Fig. 8. VSWC maps using ordinary kriging. The top two rows and bottom two rows represent the results from 21 and 25 July, respectively. The VSWC maps of the 20–40, 40–60, 60–80 and 80–100 cm depths are deduced by Eq. (2). Table 3 Statistics of the GPR-derived VSWC computed for nine depth ranges. Depth (cm)

0–20 0–40 0–60 0–80 0–100 20–40 40–60 60–80 80–100

VSWC before rainfall (m3 m−3)

CV (%)

Minimum

Maximum

Mean

STD

0.166 0.167 0.194 0.205 0.184 0.168 0.224 0.150 0.102

0.330 0.400 0.344 0.335 0.332 0.470 0.346 0.362 0.336

0.255 0.269 0.272 0.275 0.276 0.282 0.279 0.284 0.282

0.012 0.020 0.022 0.024 0.026 0.029 0.027 0.034 0.032

4.7 7.5 8.0 8.9 9.2 10.1 9.6 11.8 11.2

VSWC after rainfall (m3 m−3)

CV (%)

Minimum

Maximum

Mean

STD

0.170 0.171 0.196 0.205 0.185 0.172 0.127 0.110 0.103

0.339 0.412 0.344 0.335 0.332 0.530 0.346 0.362 0.336

0.272 0.299 0.300 0.300 0.300 0.327 0.299 0.303 0.298

0.013 0.025 0.019 0.014 0.012 0.039 0.020 0.027 0.023

4.7 8.3 6.2 4.7 4.0 11.8 6.6 8.9 7.7

uptake by roots (Starks et al., 2006; Nippert et al., 2012; Fang et al., 2016; Wang et al., 2019). Citrus roots are densely distributed and have a wide water absorption range, which is consistent with the findings of Lu et al. (2017), who observed a high average soil water content in the depth range of 0–42 cm. Meanwhile, soil moisture is also affected by the crown canopy, which can effectively reduce evaporation in agricultural fields. Rainfall is intercepted and redistributed by the crop canopy as it moves toward the ground. In recent years, many studies have found that the rate of canopy interception ranges from 11.4% to 34.3% in different vegetation types (Murakami and Toba, 2013; Sun

lines using the GPR ground wave method. In addition, through the transformation function (Eq. (2)), VSWC difference maps of 20–40, 40–60, 60–80 and 80–100 cm could be obtained. As shown in Fig. 8, the mean VSWC of the entire 0–40 cm solum can be expected to be considerably lower at altitudes of 56–58 m than at high and low altitude areas with low vegetation coverage. The differences in the mean VSWC values in the orchard were less than those in the upland region at the depth ranges of 0–20 and 20–40 cm (Table 5). These differences could be attributed to the effects of vegetation on rainfall redistribution processes, such as canopy interception and water 8

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0~20 cm

0~40 cm

0~60 cm

0~80 cm

0~100 cm

20~40 cm

40~60 cm

60~80 cm

80~100 cm

Fig. 9. The spatial distribution of the difference between VSWC after rainfall and VSWC before rainfall at nine soil depth ranges. Negative values indicate a decrease in VSWC, and positive values indicate an increase.

4.7% to 9.2% for depths ranging from 0–20 to 0–100 cm (Table 3). It seems plausible that the VSWCs in deep soil varied substantially more than those in topsoil. However, the VSWCs at 20-cm intervals below the surface soil exhibited similar variations with CVs varying from 9.6% to 11.2%. The great CVs of the 0–80 and 0–100 cm layers could be jointly ascribed to the relatively poor fitting between the dielectric constant and VSWC (Eqs. (8) and (9)) and slightly high STDs of VSWCs at depths of 60–80 and 80–100 cm (Table 3). The CVs of the VSWC after rainfall generally decreased as the depths ranged from 0–20 to 0–100 cm or declined per 20-cm (Table 3). The changes in the CV along the soil profile could be partly attributed to the maximal soil water content in

and Wang, 2014). The VSWC difference in the 20–40 cm depth was characterized by high mean values in the upland region (0.048 m3 m−3) and orchard (0.041 m3 m−3) (Table 5). This result suggests that the rainwater mainly concentrated in this layer and gradually infiltrated the subsoil due to increasing soil compaction (Table 1). Regarding the spatial distribution, which Tahir et al. (2016) mentioned, we generally can anticipate a high VSWC and suitable growing environment for plants at the bottom of a slope. Rainfall events greatly affected the vertical variations in soil water content (Table 3). The CVs of the VSWC before rainfall increased from

0.25 y=0.172x+0.217 RMSE=0.046 R2=0.501

0.20

0.20

0.25

0.30

0.35

(d) 0.40

F0_80

0.30

0.25

0.15 0.15

y=0.355x+0.182 RMSE=0.032 R2=0.395 0.20

0.25

0.30

0.35 3

-3

VSWC measured by TDR (m m )

y=0.447x+0.153 RMSE=0.027 R2=0.725

0.20

(e) 0.40

0.35

0.20

0.25

0.20

0.25

0.30

0.35 3

1:1

0.40

1:1

0.30

0.15 0.15

0.40

F0_40

0.35

-3

VSWC measured by TDR (m m ) Before rainfall After rainfall

Before rainfall After rainfall

0.40

F0_100

Before rainfall After rainfall

F0_60

1:1

0.35

0.30

0.25 y=0.445x+0.155 RMSE=0.028 R2=0.578

0.20

0.15 0.15

0.20

0.25

0.30

0.35

0.40

VSWC measured by TDR (m3 m-3)

-3

VSWC measured by TDR (m m ) Before rainfall After rainfall

VSWC predicted by GPR (m3 m-3)

0.30

3

VSWC predicted by GPR (m3 m-3)

1:1

VSWC predicted by GPR (m3 m-3)

F0_20

0.35

0.15 0.15

(c) 0.40

(b) 0.40 Before rainfall After rainfall

VSWC predicted by GPR (m3 m-3)

VSWC predicted by GPR (m3 m-3)

(a) 0.40

1:1

0.35

0.30

0.25 y=0.369x+0.183 RMSE=0.031 R2=0.335

0.20

0.15 0.15

0.20

0.25

0.30

0.35

0.40

VSWC measured by TDR (m3 m-3)

Fig. 10. Validation graphs of the spatial prediction in the field. Corrected data were used for the VSWCs measured by TDR. The validation indices in each plot refer to the overall indices. 9

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Table 4 Validation indices of the VSWC predicted for different soil depths before and after rainfall. Depth (cm)

0–20 0–40 0–60 0–80 0–100

RMSE (m3 m−3)

R2

r Before rainfall

After rainfall

Overall

Before rainfall

After rainfall

Overall

Before rainfall

After rainfall

Overall

0.664 0.762 0.894 0.678 0.646

0.658 0.774 0.518 0.387 0.329

0.713 0.854 0.765 0.636 0.588

0.422 0.567 0.793 0.442 0.398

0.413 0.587 0.244 0.122 0.078

0.501 0.725 0.578 0.395 0.335

0.040 0.026 0.025 0.028 0.027

0.052 0.028 0.031 0.037 0.035

0.046 0.027 0.028 0.032 0.031

inversion errors were as high as 0.10 m3 m−3 (Sambuelli, 2009; Steelman and Endres, 2011). Measurement accuracy may be affected by the soil sampling methods of the ground-truth VSWC value. Huisman et al. (2001) demonstrated that the RMSE between GPR and TDR was 0.03 m3 m−3, and Lunt et al. (2005) found that the VSWC variability of 0.018 m3 m−3 was measured by the neutron method with GPR using the ground wave method. In the current study, the real VSWC could be best represented by TDR, which was calibrated by the gravimetric method. The overall RMSE could be considered to be the sum of GPR measurement uncertainty before and after rainfall. From the visualization of the predicted results, greater RMSE values were obtained on 25 July than on 21 July (Table 4). The greater the VSWC was, the greater the RMSE and the worse the inversion effect. The general trend was consistent with the findings of Giroux and Chouteau (2010), who showed that highly conductive soil conditions may result in a poor result regarding GPR inversion. In addition, precipitation may have an impact on the reflection of radar waves due to high soil water contents.

Table 5 Comparison of VSWC differences at five depth ranges under different land use types. Depth (cm)

Land use type

VSWC difference (m3 m−3) Minimum (m3 m−3)

Maximum (m3 m−3)

Mean (m3 m−3)

STD (m3 m−3)

CV (%)

0–20

Upland Orchard

−0.008 −0.006

0.059 0.043

0.019 0.014

0.009 0.009

48.6 64.0

20–40

Upland Orchard

−0.021 −0.014

0.165 0.120

0.048 0.041

0.024 0.020

50.6 49.4

40–60

Upland Orchard

−0.059 −0.012

0.103 0.087

0.034 0.032

0.031 0.020

90.5 61.7

60–80

Upland Orchard

−0.131 −0.059

0.108 0.103

0.025 0.034

0.039 0.031

156.2 90.5

80–100

Upland Orchard

−0.109 −0.055

0.127 0.118

0.023 0.022

0.039 0.033

165.6 152.9

5. Conclusions the 20–40 cm layer. In this area, the most intense evapotranspiration was found in July (Tahir et al., 2016), which acted as the main hydrological process before rainfall and could consume more water from topsoil (Gao et al., 2015), and deep soil water frequently interacted with groundwater, of which the level was approximately 2–3.5 m (Gao et al., 2015). Therefore, the VSWCs observed before rainfall events were slightly greater in deep soil than in topsoil. There were exceptions for the VSWC changes after rainfall events, such as the slight declines in the 40–60 and 80–100 cm depth ranges (Fig. 6a). This result might be comprehensively explained by the spatiotemporal variability of the VSWC (Gao et al., 2016), the high soil water content at depths of 20–40 cm after rainfall (Table 3) and the increasing soil compaction in deep soil that prohibited rapid infiltration. Even so, the overall VSWC along the soil profiles increased after a rainfall event (Fig. 6b), which was consistent with the general understanding of the significant impact of precipitation on soil moisture variations in humid or semihumid areas (Gao et al., 2015; Fang et al., 2016; Wang et al., 2019).

In this research, petrophysical relationships down to soil depths of 1 m were quantified based on 32 CMP soundings and TDR measurements. Furthermore, VSWC maps of a 3.2 ha agricultural field before and after rainfall were generated based on GPR data from the ground wave method. Validation indices showed that the VSWC prediction based on geostatistical methods appeared to be precise and consistent with the TDR values. Both before and after rainfall, the topography and land use types had an obvious impact on the VSWC spatial distribution. By assessing the sources of errors in VSWC mapping, we found that precipitation increased the VSWC, which greatly changed the propagation path of the electromagnetic wave and further intensified the uncertainty of the ground wave method. The enhanced ground wave technique for VSWC monitoring and predictive mapping shows promising potential at the field scale and compensates for the shortcomings of traditional sampling methods and remote sensing methods. In particular, this technique may contribute to managing water resources effectively, increasing crop yields and promoting the development of precision agriculture.

4.3. GPR-derived VSWC validations Declaration of Competing Interest The high accuracy of the ground wave method for the estimation of the surface VSWC was determined from an exact and suitable empirical relationship. To improve the VSWC estimation accuracy, we proposed an empirical function for each depth range. In this way, the overall performance was obviously improved. Notably, the inversion results of the 0–40 cm depth yielded the best performance (R2 = 0.725). The R2 of our fitted models was over 0.47 (Eqs. (5)–(9)), and the overall accuracy of the VSWC maps was acceptable (Fig. 10), which were better than or comparable to those in related studies (Reza and Ardekani, 2013; Barker et al., 2017). Even so, there were still some limitations. As discussed in Section 4.1, appropriate empirical models may require more data at the regional scale. Furthermore, even if we calibrated the empirical models with field GPR data, the VSWC

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The study was financially supported by the National Natural Science Foundation of China (grant Nos. 41571130051, 41771251 and 41977003) and partly by the National Key Research and Development Plan of China (No. 2018YFE0107000). Acknowledgments are also extended to Chen Zhong and Xinxin Chen for their technical help during the GPR survey. 10

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